Dear Phil,

It is good to see your contribution. I always enjoy your insight.

You mention that since the 1970s all work on theoretical physics including supersymmetry and string theory has failed to make contact with experiment. I think that you attribute this to a dearth of new experimental results at the energy frontier. An alternative possibility is a theory that predicts what we see and nothing else.

As I understand it, you believe the appropriate starting point for a theory of theories is modeled as a formal sum of the collection of mathematical universes; that is, every mathematical possibility has a corresponding physical possibility (more or less). I think you have explored this approach quite well.

An alternative approach would begin with one physical field, and nothing else, and attempt to derive our current universe from this field. That happens to be my preferred approach. I believe it is compatible with your answer that "up to energies tested so far there was simply "nothing new". I recall particle physicists a decade ago being sort of upset by the suggestion that the only particles that exist are those we know and resonances composed of those that we know. In fact I suggested that the Higgs was not a fundamental particle but just such a resonance. After several years of celebrating the Higgs, the latest Phys Rev Letters papers that I have seen are those analyzing Higgs as 'composite particle'.

You state: "in my opinion they are failing because they still cannot relinquish certain cherished philosophical beliefs." I fully agree with you. Now we just have to agree on the cherished beliefs in question!

My own belief is that the answer is more likely to come from the extreme that you explore, or the opposite extreme that I explore, than it is to come from anywhere in the middle.

My best regards, and good luck.

Edwin Eugene Klingman

    Dear Philip,

    I am very happy to see you entering a contribution into this year's competition, your essays are always enlightening to read, and provide much food for thought.

    The idea of a 'Theory of Theories' is something I have been spending a bit of intellectual energy on, as well, mostly inspired by Russell Standish's 'Theory of Nothing' and Jürgen Schmidhuber's 'Algorithmic Theories of Everything' (see here: https://arxiv.org/abs/quant-ph/0011122). Schmidhuber's approach in particular seems at first blush not too distant from your own---he also appeals to Kolmogorov complexity in the construction of a (formally describable) measure, over possible histories of the universe.

    But I have only skimmed your paper as of yet; I'll revisit it when I get some more time, and look forward to engaging with it in detail.

    I wish you the best of luck in this contest!

      Thank you to all those who have responded already. Today really is my 60th birthday so I am off to see family.

      I always relish the opportunity to enter these contests because the feedback I get and the comparison with other essays is pure gold. My ideas always take a quantum leap forward as a result.

      I will respond to specific comments and read other submissions when I get back.

        Edwin,

        You nailed it:

        "An alternative possibility is a theory that predicts what we see and nothing else."

        That is exactly what existing quantum theory does, which is why it has always been misinterpreted - it only (but accurately) predicts the detection statistics of a test, for the presence of "something", rather than describing either the "something" itself, or even how the "something" behaves. It is analogous to accurately predicting that a "drug test" will detect "something", but without ever bothering to consider the likelihood of all the "false positives".

        "Now we just have to agree on the cherished beliefs in question!"

        Start with the 2,500 year old, ancient, Greek philosophical assumption that "elementary" particles must all be perfectly identical, while taking note of the fact that some [link:vixra.org/abs/1609.0129#comment-4458485189]"fraternal twins" do not behave anything like "identical twins"[/link] in a Bell test. Next, consider the fact that a single Fourier transform (superposition/wavefunction) cannot be used to correctly describe more than one single particle trajectory, at a time, in the presence of any noise; assuming (as quantum theorists did, in the 1920s) that you ought to be able describe multiple particles, via a single superposition, was a huge misconception - that "trick" only works correctly, in an idealistic (AKA unreal) noise-free situation.

        Rob McEachern

        Happy Birthday Phil!

        I have not read the essay yet, but I have been a fan of this line of reasoning for years now. The notion that what makes sense physically would emerge from the spectrum of all possible theories naturally is a compelling idea. When I was struggling to find a proper context for my work - when I first began to see the relevance of the Mandelbrot Set to Physics - the 'theory of theories' notion put things into focus very nicely; thank you.

        I hope you find renewed vigor and increased confidence with year 60. I was told a story by Joe Lam on my 59th birthday that he thought he'd be washed up at 60 but found the opposite instead, that he had more self confidence and had new horizons opening up - so his life picked up speed. That was the night I had the pleasure to meet and eat with Leo KoGuan, Brian Greene, Paul Joskow, fellow FQXi essayist Brian Ji and also met Ed Witten.

        And as with Joe Lam; my life has only picked up speed after 60.

        All the Best,

        Jonathan

          While I hope you're off celebrating your birthday, let me just quickly add a couple of questions:

          Why do you restrict your notion of algorithm to those with finite output? It seems to me that a computer enumerating the digits of pi in succession is executing a perfectly sensible algorithm.

          What do you think the significance of the Wick rotation is? I can grasp it in the sense of 'Euclideanizing' the path integral, but it's still not fully clear to me what it means, and what one actually does when, like you do, one just Wick rotates an expression to arrive at a quantum version. (Which, by the way, I thought was a little quick; it seems to me that a little more is needed for the emergence of quantum mechanics. In particular, just a complex Hilbert space doesn't suffice, as shown by the Koopmann-von Neumann formulation of classical mechanics. But then, it's a finite-length essay, and I can't really expect you to resolve everything in one fell swoop...)

          "Although we think of data as quantised in discrete bits, information is actually a continuous quantity with no minimum value." Should we believe Kolmogorov or Fredkin?

          Robert Wright stated, "I talked with Richard Feynman, a Nobel laureate at the California Institute of Technology, before his death, in February. Feynman considered Fredkin a brilliant and consistently original, though sometimes incautious, thinker. If anyone is going to come up with a new and fruitful way of looking at physics, Feynman said, Fredkin will."

          "Did the Universe Just Happen?" by Robert Wright, The Atlantic Monthly, April 1988

          Consider 3 questions: Does quantum information reduce to Fredkin-Wolfram information? Is Milgrom the Kepler of contemporary cosmology? What is the simplest way of modifying Einstein's field equations? Google "milgrom fredkin wolfram".

            Phillip,

            Your essay was interesting. I appreciated the description in the supplement of what is meant by the necklace. Also your discussion on Turing's theorem is a nice compact version of that.

            I have some points of difference with it. I would say a departure is with the implication of some sort of infinitude. I think that for any observer the number of quantum states available for observation is finite. We may think of the horizon of a black hole with S = kA/4â„"_p^2 = NK for N the number of Planck unit quantum states. The Bekenstein bound and related results imply the number of quantum states available to an observer is finite. So even if the global Hilbert space is infinite dimensional any observer can witness only a finite subset. That might be where the necklace or enveloping algebra can come it, where this could be some general form of separable set of states in tensor products. This may in principle extend infinitely, but any observer has access to a finite quantity. The existence of horizons is a way that Hilbert space available for measurement is finite but unbounded.

            Your approach makes the implicit assumption that action = entropy, which is in a Euclideanized time sense t â†' it = ħβ = ħ/kT.the path integral maps into a partition function, where an energy E of a system is computed according to all possible combinations of microstate energies. This is a form of integer partition function. The only extension I can think of is where the measure μ(U) = e^{-S(U)} needs to be extended to μ(U) â†' μ(U)/diff(G), where G is the group of diffeomorphisms of U. However, this action = entropy or an equivalency between

            TdS = dW + dU â†" dS = pdq - Hdt,

            links quantum information with entropy

            My essay concerns how Gödel incompleteness is associated with different entanglement geometry. A heuristic comparison would be with Nagel and Newman's book on Gödel's theorem and Euclid's fifth axiom. The undecidability of the fifth axiom leads to two possible model systems for geometry, Euclidean flat space vs more general geometries of Gauss, Lobachevski and Riemann. This is a case of consistency and incompleteness vs inconsistency vs completeness. Loosely we can think of the Euclidean case as consistent but incomplete, while the more general geometries are more complete, but not consistent with each other. This without details of ω-completeness/consistency is how different entanglements have different topologies.

            Szangolies describes this as an epistemic horizon. His paper is worth reading. This has I think connections with my work through the locality of solutions for Diophantine equations, or equivalently p-adic sets.

            At any rate the part about the measure μ(U) â†' μ(U)/diff(G) as mod-diffeomorphisms I think is important. This is in gauge theory these diffeomorphisms are what define a moduli. The moduli space describes the topology such as the ADMH construction. In a duality gauge theory â†" entanglement symmetry, here on the right hand side in a SLOCC meaning, there may be a correspondence between topology of entanglement with gauge fields and topological gauge fields.

            Anyway, things to think about. I would like to see what you think of my paper.

            Cheers LC

              I will leave others to decide if my work should be interpreted as computational art, but I can try to answer both questions anyway.

              My motivation is the observation that reductionism must ultimately fail. Each time your knowledge is reduced to something more fundamental a new set of how and why questions arises. Let's not pretend that we are not trying to answer that kind of question, of course we are.

              So reductionism must be abandoned at some point, perhaps from the start. Instead we must look at the whole, at what information and experience is. Everything must be equally real or unreal, but reality is relative to the observer.

              This conclusion then provides the problem I am trying to solve. How can our experience of physics arise from that starting point? Many physicists talk about how information is fundamental, and reality must be emergent. If you assume that space and time emerge then perhaps you can argue for gravity as an emergent entropic force, but what about the deeper origins? How do we get from pure information and self-reference to space and time and some real physics? I want to go beyond all this nice philosophy and actually so something with the maths.

              If I tell you that a random three digit number is even I have given you one bit of information. If I tell you only that it is not 137 I have given you much less information.

              Quantum theory leaves open the possibility of a deterministic underlying theory but it requires a big stretch. Everything suggests the opposite, but if your philosophical position is that reality must be deterministic then by all means try to exploit the loop holes. I wish you luck.

              I hope you will submit a good essay to support your case and I look forward to it.

              You cannot transmit (and thus give to me) the first sentence you stated, in a message only one bit in length. The same is true of your second sentence. Your conception of "information", differs substantially, from that of Shannon. Luck is not necessary, where understanding is sufficient. An essay is not necessary to support my case, since a sufficient demonstration has already been published. Q.E.D.

              Rob McEachern

              "An alternative possibility is a theory that predicts what we see and nothing else."

              What we see includes the standard model of particles, neutrino masses, gravity, galaxy rotation curves etc. Theorists don't set out to find models that add more to the list. They just look for models that provide a consistent framework for some or all of these things together. It may turn out that those models have additional particles or other observable or unobservable effects, and this is often the case. These additional things provide some testability, but if they found a consistent model for everything that had nothing new I am sure we would all be equally happy with it.

              You are right that I start with an ensemble of possible universes. The way I differ from the usual MUH is that I think these different universes combine into a single whole that is accessible in our reality. According to the MUH we live in just one mathematical external reality. I think my approach may be closer to yours. My "multiverse" of universes is actually indistinguishable from the "multiverse" of wavefunctions in quantum mechanics which is really just one field.

              Dear Philip E. Gibbs,

              "Information is the basic material of reality, but the processing of information raises paradoxes due to the self-referential nature of computability."

              Perhaps I overlooked this statement and something that may substantiate it at the beginning, the end or even any part of your essay on "Undecidability ..."

              I was lazy and looked for where you referred to [ 4] Shannon at your p. 2. Maybe you merely corrected Shannon by mentioning that the DNA is a material code. Otherwise, one is tempted to read your theory of theories as new-Hegelian idealism. Anyway, I see you obliged to take McEathern's critical arguments more seriously. He is complaining at my own essay.

              Eckard Blumschein

                Thanks for your comments, references and questions.

                You make a fair point that when defining computability, infinite strings of output are required. Any finite string is computable. However for the halting problem it is easier to work with just finite output. The computation of a universe might make more sense if it is allowed to be infinite, but I am not sure I could have cleared this up in the limited space.

                For the Wick rotation I accept that this was too quick. Working with probabilities between 0 and 1 is not very good when trying to define and algebra so a switch to complex numbers works better. More work would be required to determine whether this is justified in that it would give an equivalent formulation.

                The amount of information conveyed by a statement is not the bit-length of the string that communicates it. That only sets an upper limit. What I have said at the start about information content is standard stuff, but a lot of people have a misconception that information always comes in discrete bits so I had to explain that it doesn't. It is covered in wikipedia at https://en.wikipedia.org/wiki/Information_content

                The negative log of a probability gives the information content for the outcome of a random process and it can take any real value from zero to infinity.

                That information is the basic material of reality is an axiom here. I would justify it by observing that everything is described by information in physics, mathematics and any other subject. I don't need any other substrate as a foundation and seek to derive everything else from information alone.

                I am not an expert on the classifications used by philosophers but I find much in common with both Hume and Kant and others. I would say that the underlying structure of our reality can be derived from the way we must experience it in terms of processing uncertain information. Probably this is some form of idealism but I am not sure which variety it is.

                "What I have said at the start about information content is standard stuff..." In Algorithmic Information theory, but it has little to do with Shannon's Information theory.

                As Shannon states in the first sentence of his A Mathematical Theory of Communication, he is concerned with:

                "various methods of modulation... which exchange bandwidth for signal-to-noise ratio... in a general theory of communication."

                In other words, a trade-off (exchange) can be made, that increases bandwidth in order to offset the effect (on information capacity) of a decreased signal-to-noise ratio and vice-versa. That is what he is interested in characterizing.

                On page 43, where he gives his famous Capacity theorem (Theorem 17), he states: "This means that by sufficiently involved encoding systems we can transmit binary digits at the rate (C) bits per second, with arbitrarily small frequency of errors."

                Thus, unlike any other "flavor" of "Information theory", Shannon is primarily concerned with the circumstances, under which one can correctly (without errors) recover the values of each, individual bit, encoded into a continuous, noisy waveform. It is meaningless to talk about the error-free value, of an unrecoverable fraction of a bit, precisely because a fraction-of-a-bit has no "correct" value.

                The significance of this, is that it pertains directly to "uncertainty" in physics. Namely what is the maximum number of discrete (quantized) bits of information, that can ever be recovered, without any errors, from any set of measurements of any continuous function/signal, that has a limited duration, bandwidth and signal-to-noise ratio (SNR)? In other words, what is the maximum number of bits, that you can ever be "certain" of, in measurements of any received "signal"? What happens if that maximum number happens to be exactly equal to one? What happens is - you get the Heisenberg Uncertainty principle. That is the origin of the HUP. It has nothing to do with any "weird physics", it is simply a property of any mathematical function, with a severely limited duration, bandwidth and SNR; the very properties that Shannon said he was concerned with, in his very first sentence. There are circumstances for which, there is no possible "exchange of bandwidth for signal-to-noise ratio", that will ever enable an observer to be certain of the value of any more than one, single-bit-of-information, within an entire set of measurements, of some continuous signals. That is what "entanglement" is all about.

                Rob McEachern

                Hegel (1770-1831) strongly rejected the atomism: "The atomists are thinking too materialistic". Materialism was seen close to atheism. Maybe believer in God feel attracted from your idealism.

                On your p.8 you stated like an axiom: "Physicists have so far failed ... because they still cannot relinquish certain cherished philosophical beliefs ... objective physical reality ... and causality".

                I am ready to agree concerning reality because I see it just a successful conjecture. However by questioning causality you lost me. Aren't you aware what you are saying with words like process and processing?

                Have you any idea how to apply your axioms?